Values of Rokhlin dimension for actions of compact groups

TL;DR

This paper investigates the Rokhlin dimension for actions of finite and compact Lie groups on certain C*-algebras, demonstrating the existence of actions with arbitrarily large Rokhlin dimension and exploring its relation to the G-index.

Contribution

It establishes the existence of group actions with large Rokhlin dimension on AF and AH algebras and relates Rokhlin dimension to the G-index for compact Lie group actions.

Findings

Finite groups can act on simple AF algebras with arbitrarily large Rokhlin dimension.

Compact Lie groups can act on AH algebras with no dimension growth with large Rokhlin dimension.

Rokhlin dimension is related to the G-index for actions on commutative C*-algebras.

Abstract

We show that any finite group admits actions on simple AF algebras with unique trace which have arbitrarily large finite values of Rokhlin dimension with commuting towers. We show similar results for actions of compact Lie groups, with AH algebras with no dimension growth in place of AF algebras. We also relate Rokhlin dimension to the G-index for actions of compact Lie groups on commutative C*-algebras.